Partitioning a multi-weighted graph to connected subgraphs of almost uniform size

Takehiro Ito; Kazuya Goto; Xiao Zhou; Takao Nishizeki

doi:10.1007/11809678_9

Partitioning a multi-weighted graph to connected subgraphs of almost uniform size

Takehiro Ito, Kazuya Goto, Xiao Zhou, Takao Nishizeki

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Assume that each vertex of a graph G is assigned a constant number q of nonnegative integer weights, and that q pairs of nonnegative integers l _i and u_i, 1 ≤ i ≤ q, are given. One wishes to partition G into connected components by deleting edges from G so that the total i-th weights of all vertices in each component is at least l_i and at most u_i for each index i, 1 ≤ i ≤ q. The problem of finding such a "uniform" partition is NP-hard for series-parallel graphs, and is strongly NP-hard for general graphs even for q = 1. In this paper we show that the problem and many variants can be solved in pseudo-polynomial time for series-parallel graphs. Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width.

Original language	English
Title of host publication	Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings
Publisher	Springer Verlag
Pages	63-72
Number of pages	10
ISBN (Print)	3540369252, 9783540369257
DOIs	https://doi.org/10.1007/11809678_9
Publication status	Published - 2006
Event	12th Annual International Conference on Computing and Combinatorics, COCOON 2006 - Taipei, Taiwan, Province of China Duration: 2006 Aug 15 → 2006 Aug 18

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4112 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	12th Annual International Conference on Computing and Combinatorics, COCOON 2006
Country/Territory	Taiwan, Province of China
City	Taipei
Period	06/8/15 → 06/8/18

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/11809678_9

Cite this

Ito, T., Goto, K., Zhou, X., & Nishizeki, T. (2006). Partitioning a multi-weighted graph to connected subgraphs of almost uniform size. In Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings (pp. 63-72). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4112 LNCS). Springer Verlag. https://doi.org/10.1007/11809678_9

Partitioning a multi-weighted graph to connected subgraphs of almost uniform size. / Ito, Takehiro; Goto, Kazuya; Zhou, Xiao; Nishizeki, Takao.

Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings. Springer Verlag, 2006. p. 63-72 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4112 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ito, T, Goto, K, Zhou, X & Nishizeki, T 2006, Partitioning a multi-weighted graph to connected subgraphs of almost uniform size. in Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4112 LNCS, Springer Verlag, pp. 63-72, 12th Annual International Conference on Computing and Combinatorics, COCOON 2006, Taipei, Taiwan, Province of China, 06/8/15. https://doi.org/10.1007/11809678_9

Ito T, Goto K, Zhou X, Nishizeki T. Partitioning a multi-weighted graph to connected subgraphs of almost uniform size. In Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings. Springer Verlag. 2006. p. 63-72. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11809678_9

Ito, Takehiro ; Goto, Kazuya ; Zhou, Xiao ; Nishizeki, Takao. / Partitioning a multi-weighted graph to connected subgraphs of almost uniform size. Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings. Springer Verlag, 2006. pp. 63-72 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Partitioning a multi-weighted graph to connected subgraphs of almost uniform size

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